Past Events

Random regular graphs form a ubiquitous model for chaotic systems. However, the spectral properties of their adjacency matrices have proven difficult to analyze because of the strong dependence between different entries. In this talk, I will describe recent work that shows that despite this, the…

We consider a class of Lagrangians living in \mathbb{C}^3 . Their Ekholm-Shende wavefunctions, living in the HOMFLY-PT skein module, will encode open Gromov-Witten invariants in all genus and arbitrarily many boundary components. We develop a skein valued cluster theory to…

Mordell (1922) proved that the rational points of an elliptic curve $E / {\bf Q}$ form a finitely-generated abelian group. It is still not known which finitely-generated abelian groups can occur as $E({\bf Q})$. Mazur (1977) proved that the possible torsion subgroups $T$ are the cyclic groups of…

I swear I've heard this before... Wait. Wait wait wait. No way! These drums sound exactly the same! And you're telling me you have a systematic way of constructing these?? That's craaaaaazy.

I will cover the method of establishing superconcentration via hypercontractive inequalities with two examples: Talagrand's Gaussian L1-L2 inequality and the KKL inequality for Boolean functions. The basic definitions and identities involving semigroups and the dirichlet form will be covered for…

We will prove the global existence and uniqueness of solutions to the Cauchy problem for the Boltzmann equation of a hard sphere, assuming small data. We will also show that such solutions, assuming nonnegative initial data, remain nonnegative, which is what we expect, as a solution represents a…

The local volume of a Kawamata log terminal (klt) singularity is an invariant that plays a central role in the local theory of K-stability. By the stable degeneration theorem, every klt singularity has a volume preserving degeneration to a K-semistable Fano cone singularity. I will talk about a…

Around 10 years ago, Donaldson and Sun discovered that metric limits of Ricci positive Kähler–Einstein manifolds are algebraic varieties, and their metric tangent cones also underlie some algebraic structure. I will talk about a general algebraic geometry theory behind this phenomenon. In…

Look at a typical partition of N (uniform distribution). What does it 'look like'? How many singletons, parts of size k, how big is the largest part? AND how can we generate such a random partition, say when N = 10^6, to check theory against 'reality'    Of course, there are many…

We consider properly immersed two-sided stable minimal hypersurfaces of dimension n. We illustrate the validity of curvature estimates for n \leq 6 (and associated Bernstein-type properties with an extrinsic area growth assumption). For n \geq 7 we illustrate sheeting results around "flat…